Beyond Mandatory Federations: Balancing Egoism, Utilitarianism and Egalitarianism in Mixed-Motive Games

In the field of mixed-motive games, extensive multi-agent learning studies have explored the balance between egoism (individual interest), utilitarianism (collective interest), and egalitarianism (fairness). Traditional approaches often rely on manually designed reward functions, social norms, and alliance/federation mechanisms to transition agents from individualistic behaviors toward cooperative strategies. However, these methods typically require all agents to share private local information or to mandatorily participate in federations, which is impractical in real-world applications. To address these issues, this paper proposes a Flexible-Participation Federation (FPF) framework that allows agents to participate in the federation voluntarily. Furthermore, we extend the federation from a global to a Local Multi-Federation (LMF) framework, enabling agents to form multiple localized federations, thereby promoting more efficient and adaptive cooperation. Theoretical evidence demonstrates that the global FPF model, along with the discrepancy between decentralized egoistic policies and federated utilitarian policies, achieves an O(1/T) convergence rate. Agents in the LMF framework also reach consensus within a sublinear gap. Extensive experiments show that agents opting out of federation participation experience a reduction in egoism, and our approach outperforms multiple baselines in terms of both utilitarianism and egalitarianism.